Discussion
Which of the following statements is always true for Poisson distribution ?
Answer: B
For a Poisson distribution, mean = variance.
A Poisson distribution with parameter \(\lambda\) has mean \(\lambda\) and variance \(\lambda\), so the two are always equal. This is its distinguishing property, and it is used to check whether count data fit a Poisson model.
Mean greater than variance is the binomial case, mean less than variance is typical of the negative binomial, and the standard deviation is \(\sqrt{\lambda}\), which equals the mean only when \(\lambda = 1\).
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